Factoring Trinomials Calculator
Factor quadratic trinomials using the AC method with step-by-step solutions
Quadratic Trinomial
Current Trinomial:
Standard form: ax² + bx + c
Factorization Result
Factored Form
Step-by-Step Solution
Example Problems
Example 1: Simple Case (a = 1)
Trinomial: x² + 8x + 12
AC Method: Find two numbers that multiply to 12 and add to 8
Pair: 2 * 6 = 12, 2 + 6 = 8
Result: (x + 2)(x + 6)
Example 2: General Case
Trinomial: 2x² + 7x + 3
AC Method: AC = 2 * 3 = 6, find pair that adds to 7
Pair: 1 * 6 = 6, 1 + 6 = 7
Result: (2x + 1)(x + 3)
Example 3: Perfect Square
Trinomial: x² + 6x + 9
Pattern: a² + 2ab + b² = (a + b)²
Result: (x + 3)²
AC Method Steps
Calculate AC
Multiply coefficients a and c
Find Factor Pairs
List all pairs that multiply to AC
Check Sums
Find pair that adds to coefficient b
Factor by Grouping
Rewrite and factor the expression
Quick Tips
Understanding Trinomial Factoring
What is a Quadratic Trinomial?
A quadratic trinomial is a polynomial of degree 2 with three terms, written in the form ax² + bx + c where a, b, and c are real numbers and a ≠ 0. Factoring means finding two linear binomials that multiply to give the original trinomial.
The AC Method
The AC method (also called factoring by grouping) is a systematic approach to factor quadratic trinomials. It involves finding two numbers whose product equals AC and whose sum equals B, then using these to rewrite and factor the expression.
Special Cases
Perfect Square Trinomial
a² + 2ab + b² = (a + b)²
Difference of Squares
a² - b² = (a + b)(a - b)
Common Factor
Factor out GCD first, then proceed
When Can't We Factor?
Negative Discriminant
When Δ = b² - 4ac < 0
No Integer Factors
No integer pair satisfies the conditions
Irrational Roots
Roots exist but are not rational